Julie Pace and Will Weissert, The Associated Press
Published Saturday, February 13, 2016 11:21PM EST
Last Updated Sunday, February 14, 2016 8:03AM EST

GREENVILLE, S.C. -- Republican White House hopefuls called for President Barack Obama to step aside and allow his successor to nominate the next Supreme Court justice, in a debate jolted by Saturday's death of conservative Justice Antonin Scalia.

Only Jeb Bush said Obama had "every right" to nominate a justice during his final year in office. The former Florida governor said there should be "consensus orientation on that nomination" -- but added that he didn't expect Obama would pick a candidate in that vein.

The five other candidates on the stage Saturday urged the Republican-led Senate to block any attempts by the president to get his third nominee on the court.

Just six contenders took the debate stage in South Carolina, far from the long line of candidates who participated in earlier Republican events. Yet the Republican race remains deeply uncertain, with party elites still hoping that one of the more mainstream candidates will rise up to challenge Trump and Cruz. Many Republican leaders believe both would be unelectable in November.

On the Democratic side, Hillary Clinton told a Democratic dinner in Denver that Obama has the right to nominate another justice. He "is president of the United States until Jan 20, 2017. That is a fact my friends, whether the Republicans like it or not."

"Let's get on with it," said Democrat Bernie Sanders, arguing that the Senate should vote on whoever Obama nominates.

Trump and Bush tangled in some of the night's most biting exchanges, highlighting the bad blood between the real estate mogul who leads the Republican field and the former Florida governor who was once expected to sail to the nomination. In a particularly heated confrontation, Trump accused Bush's brother -- former President George W. Bush -- of having lied to the public about the Iraq war.

"Obviously the war in Iraq was a big fat mistake," Trump said.

Bush, who has been among the most aggressive Republican candidates in taking on Trump, said that while he doesn't mind the real estate mogul criticizing him -- "It's blood sport for him" -- he is "sick and tired of him going after my family."

Trump was jeered lustily by the audience in a state where the Bush family is popular with Republicans. Former President George W. Bush plans to campaign with his brother in Charleston on Monday, making his first public foray into the 2016 race.

Candidates used Scalia's sudden death to raise the stakes for the general election.

Cruz cast the moment in stark terms, saying allowing another Obama nominee to be approved would amount to Republicans giving up control of the Supreme Court for a generation. An uncompromising conservative, Cruz urged voters to consider who among the Republican candidates would nominate the most ideologically pure justices.

Saturday's debate came one week before South Carolina's primary. Cruz and Trump emerged from the first two voting contests with a victory apiece and appear positioned to compete for a win in the first Southern primary.

Ohio Gov. John Kasich defended himself against attacks on his conservative credentials, particularly his decision to expand Medicaid in Ohio despite resistance from his Republican-led Legislature. Kasich argued that his decision was a good deal for the state in the long run.

Bush played the aggressor again, saying that Kasich's actions amounted to "expanding Obamacare" -- a deeply unpopular concept among Republicans.

Sanders, a Senator from Vermont, spoke to reporters Saturday before flying to Colorado for a Democratic dinner at which both he and Clinton appeared. He used unusually blunt words to express frustration with his opponent.

"I am really stunned by some of the attacks we are getting from Secretary Clinton," he said. "Clearly they have been unraveled by the results in Iowa, by our victory in New Hampshire and the progress we are making all over this country."